Generalised additive point process models for natural hazard occurrence

Point processes are a natural class of models for representing occurrences of various types of natural hazard event. Flexibly implementing such models is often hindered by intractable likelihood forms. Consequently, the rates of point processes tend to be reduced to parametric forms, or the processes are discretised to give data of readily modelled “count‐per‐unit” type. This work proposes generalised additive model forms for point process rates. The resulting low‐rank spatiotemporal representations of rates, coupled with the Laplace approximation, makes the restricted likelihood relatively tractable and hence inference for such models possible. The models can also be interpreted from a regression perspective. The proposed models are used to estimate different types of Cox process and then spatiotemporal variation in European windstorms. Through a combination of thin‐plate and cubic regression splines and their tensor product, established relationships between where windstorms occur and the state of the North Atlantic Oscillation are confirmed and then expanded to bring detailed understanding of within‐year variation, which has otherwise not been possible with count‐based models.